Chesapeake Energy Corp. named former ConocoPhillips Chairman Archie Dunham to lead its board as the second-largest U.S. natural-gas producer struggles with falling energy prices and mistrust of its management.

Chesapeake Energy Corp.’s decision to cut directors’ pay and other perks may save the company up to $1.65 million a year without addressing investors’ concern that the board failed to rein in Chief Executive Officer Aubrey McClendon’s borrowing and spending spree.

Chesapeake’s board backed away from a week-old endorsement of Chairman and CEO Aubrey McClendon’s practice of using personal stakes in company wells to secure loans, pledging now to investigate the transactions.